
The first two sum rules, Eqs. (REF ) and (), insure that the contributions to the scattering amplitudes growing like \({\cal O}(s^5)\)  and \({\cal O}(s^4)\)  vanish. They follow directly from the Sturm-Liouville form of the spin-2 KK mode equation, Eq. (REF ) and the corresponding completeness relation Eq. (REF )- so the proofs given in [1]}, [2]}, [3]} apply to any model producing a geometry defined by a warp function \(A(y)\) . However, the sum rules in Eqs. () and (), which insure cancellation of the contributions to the amplitude growing like \({\cal O}(s^3)\)  and \({\cal O}(s^2)\) , involve the scalar tower present in the GW model.
